# Why am I required to conduct a reverse transformation on my predicted variables?

I'm having difficulty wrapping my head around an instruction in my assignment. I would appreciate any pointers.

After transforming the mean predicted values of my simple linear regression model, I followed the instructions and ran another linear regression with my transformed dependent variable (i.e. √x). I then generated the mean predicted values for my dependent variables. My original model had a slightly better fit (R^2) than my transformed model.

This is where I am having trouble:

I was then tasked to reverse the transformation on my predicted variables (i.e. x^2 ) and interpret a predicted value at a given independent value (say y=5). My predicted value is significantly higher (over-predicting) than the one from my original regression model. I am trying to understand why that is and what was the purpose of reversing the transformation in the first place? Does it have something to do with the distribution of my residuals since I was tasked to conduct a transformation?

• Well, if the estimated model is used for predictions they presumably want predictions on the original scale. When transforming $y$, estimating and the retransforming to get predictions on the original scale, the prediction are not unbiased. That might be what you are seeing. stats.stackexchange.com/questions/215697/… – kjetil b halvorsen Sep 16 '17 at 20:09
• – kjetil b halvorsen Sep 16 '17 at 20:12